• 대한수학회지
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• 제51권2호
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• pp.325-344
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• 2014

The aim of this paper is to generalize the theory of Hopf-Ore extension on Hopf algebras to Hopf group coalgebras. First the concept of Hopf-Ore extension of Hopf group coalgebra is introduced. Then we will give the necessary and sufficient condition for the Ore extensions to become a Hopf group coalgebra, and certain isomorphism between Ore extensions of Hopf group coalgebras are discussed.

• 충청수학회지
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• 제32권2호
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• pp.191-193
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• 2019

It is shown that a left Ore extension $D[x;{\sigma}]$ over a division ring D is a left Goldie ring with no zero-divisor and that its left Goldie quotient is an injective hull of $D[x;{\sigma}]$.

• 암석학회지
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• 제21권4호
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• pp.397-403
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• 2012

홍천 자은리에 분포하는 탄산염암류 기원의 철-희토류 광화대는 북부, 중부, 그리고 남부의 3개 광체가 남-북 방향으로 단속적으로 발달하고 있는데 지질구조 분석을 통해 이들의 분포와 연장특성을 파악하였다. 북부광체 및 중부광체 일대의 편마암에서의 엽리는 북북동 방향을 보이나, 광체의 남쪽으로 가면서 북동에서 동북동 방향으로 방향이 바뀌며 남부광체 부근에서는 다시 남-북 방향을 보이고 있다. 기하학적으로 분석되는 이 일대의 습곡은 자은교에서 새마을교 까지 북서쪽으로 오목하게, 완만하게 열린 습곡(open fold)으로 습곡축이 북서쪽으로 약 $45^{\circ}$ 침강하는 향사를 이루며, 새마을교 서측의 약수터 부근에서는 습곡축이 북서 방향으로 약 $45^{\circ}$ 침강하는 소규모의 배사를 이루고 있다. 이들 습곡은 약수터에서 새마을교 쪽으로 달리는 서북서 방향의 우수향 주향이동단층에 의해 단층끌림의 효과도 받은 것으로 추정된다. 엽리의 자세로 예측되는 습곡구조를 따라 일부 새로운 광체가 확인되므로 현재 충적층으로 피복되어져 있는 자은리 남쪽 지표상에서 미확인된 광체들이 중부와 남부 광체 사이에 엽리방향과 경사를 고려하면 거꾸로 된 기억자(ㄱ) 형태로 잠두하고 있을 것으로 추정된다. 이 지역에서 구조적으로 해석된 광체의 추정연장선 파악은 광체 확보를 위한 시추 위치 선정과 매장량 산정에 중요한 역할을 할 것으로 판단된다.

• Kyungpook Mathematical Journal
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• 제59권4호
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• pp.603-615
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• 2019

Let R be an associative unital ring with an endomorphism α and α-derivation δ. The constant products of elements in Ore extension rings, when the coefficient ring is reversible, is investigated. We show that if f(x) = ∑ⁿ_i=0 a_ixⁱ and g(x) = ∑^m_j=0 b_jx^j be nonzero elements in Ore extension ring R[x; α, δ] such that g(x)f(x) = c ∈ R, then there exist non-zero elements r, a ∈ R such that rf(x) = ac, when R is an (α, δ)-compatible ring which is reversible. Among applications, we give an exact characterization of the unit elements in R[x; α, δ], when the coeficient ring R is (α, δ)-compatible. Furthermore, it is shown that if R is a weakly 2-primal ring which is (α, δ)-compatible, then J(R[x; α, δ]) = N iℓ(R)[x; α, δ]. Some other applications and examples of rings with this property are given, with an emphasis on certain classes of NI rings. As a consequence we obtain generalizations of the many results in the literature. As the final part of the paper we construct examples of rings that explain the limitations of the results obtained and support our main results.

• 대한수학회논문집
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• 제21권1호
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• pp.1-9
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• 2006

A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring, G be an ordered monoid acting on R by $\beta$ and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring $R_{\beta}[G]$ is (left principally) quasi-Baer. If G is an abelian monoid, then R is (left principally) quasi-Baer if and only if the Cohn-Jordan extension $A(R,\;\beta)$ is (left principally) quasi-Baer if and only if left Ore quotient ring $G^{-1}R_{\beta}[G]$ is (left principally) quasi-Baer.

• 대한자원환경지질학회:학술대회논문집
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• 대한자원환경지질학회 2007년도 춘계 지질과학기술 공동학술대회
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• pp.21-22
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• 2007

See Full Text

• 자원환경지질
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• 제11권4호
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• pp.143-167
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• 1978

The Sangdong tungsten (mostly scheelite) mine is located on the southern limb of a major syncline, the Hambaeg syncline, in a thick sequence of lower Paleozoic sedimentary rocks in the mideastern part of south Korea. Productive scheelite mineralization in Sangdong area is confined to one single formation, the Myobong Slate. Four major ore beds, which have an lateral extension over than 1 km and were not heavily subjected to spatial disturbance, are developed in the Myobong Formation. The original materials of the ore-comprising horizones were probably of either calcareous or silceous sediments. The four ore beds, especially in the case of Main ore bed, display both lateral and vertical zoning. Association quartz-mica-scheelite is predominant in the central, while association hornblende-quartz-diopside-scheelite, diopside-garnet and wollastonite-garnet are developed in this order towards the periphery of the ore beds. Petrologically, two phases of thermometamorphism are recognized. The first phase is represented by the association wollastonite-garnet and diopside-garnet, while the second phase by the association hornblende-quartz-diopside-scheelite and quartz-mica-scheelite. The associations of the second phase do constitute prodctive ore. The high background value of tungsten in the area surrounding the Sangdong mine reveals that the area can be considered a geochemical zone enriched in tungsten. Studies on the trace element patterns were carried out to draw useful criteria for the purpose of future geochemical exploration in the area. The increasing trend of the ratio Rb $({\times}1000)/K_2O$ of the Myobong Slate towards the known mineralization area proved to be indicative for the presence of tungsten mineralization.

• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• East Asian mathematical journal
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• 제38권1호
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• pp.1-12
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• 2022

Let R be a ring with an endomorphism σ and a σ-derivation δ. R is called (σ, δ)-Baer (resp. (σ, δ)-quasi-Baer, (σ, δ)-p.q.-Baer, (σ, δ)-p.p.) if the right annihilator of every right (σ, δ)-set (resp., (σ, δ)-ideal, principal (σ, δ)-ideal, (σ, δ)-element) of R is generated by an idempotent of R. In this paper, for a given Ore extension A = R[x; σ, δ] of R, the following properties are investigated: If R is a σ-rigid ring in which σ and δ commute, then (1) R is (σ, δ)-Baer if and only if R is (σ, δ)-quasi-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-quasi-Baer; (2) R is (σ, δ)-p.p. if and only if R is (σ, δ)-p.q.-Baer if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.p. if and only if A is (${\bar{\sigma}},\;{\bar{\delta}}$)-p.q.-Baer.

• Korean Journal of Mathematics
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• 제21권1호
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• pp.41-53
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• 2013

Antoine studied conditions which are connected to the question of Amitsur of whether or not a polynomial ring over a nil ring is nil, introducing the notion of nil-Armendariz rings. Hizem extended the nil-Armendariz property for polynomial rings onto power-series rings, say nil power-serieswise rings. In this paper, we introduce the notion of power-serieswise CN rings that is a generalization of nil power-serieswise Armendariz rings. Finally, we study the nil-Armendariz property for Ore extensions and skew power series rings.